Formal Definition For NP-completeness
There are many equivalent ways of describing NP-completeness.
Let be a language over a finite alphabet .
is NP-complete if, and only if, the following two conditions are satisfied:
- ; and
- any is polynomial-time-reducible to (written as ), where if, and only if, the following two conditions are satisfied:
- There exists such that
; and
- there exists a polynomial-time Turing machine that halts with on its tape on any input .
- There exists such that
Read more about this topic: P Versus NP Problem
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